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5 Conclusions

The goal of this review would be reached if a reasonably convincing case for an unorthodox scenario has been made. Future work will have to focus on four areas:

  1. Consolidating the existence of a non-Gaussian fixed point and that of an asymptotically safe coupling flow. This may be done in various formalisms, field variables, and approximations.
  2. Clarifying the microstructure of the geometries, identification of the antiscreening degrees of freedom, and the role of the ultraviolet cutoff.
  3. Clarifying the physically adequate notion of unitarity and its interplay with Areas 1 and 2.
  4. Characterization of generic observables and working out sound consequences for the macrophysics.


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